This chapter first attempts to model a global economic network system based on the notion of matrix-weighted graphs, the celebrated Leontief’s input–output economic model and the inter-regional input–output model described by W. Isard. Each economic system (or an agent) is represented as a vertex in the matrix-weighted graph, and each edge in the graph is associated with a corresponding nonnegative matrix weight describing a piece of multi-dimensional trade relations between different industries within a country (self-loop) or between different countries. The matrix-weighted graph provides a whole picture of the global input–output economic system. Second, the problem of determining the equilibrium price structure of the networked input–output economic system is considered for closed and open networks. In a closed model, the output of each industry is consumed by some other industries. The characteristic of a closed networked economic system is thus fully determined by its corresponding aggregated input–output matrix. In contrast, in an open model, production demands are also considered on the balancing equation relating to the input–output production vectors. Distributed algorithms are proposed to determine the solutions of the balancing equations in both models. Sufficient conditions are provided to guarantee the algorithms to asymptotically achieve the exact solution. Further, the updating algorithms also predict how the networked input–output systems would behave in the long term given a set of initial available goods.